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• Shor's_algorithm abstract "Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm (an algorithm that runs on a quantum computer) for integer factorization formulated in 1994. Informally it solves the following problem: Given an integer N, find its prime factors.On a quantum computer, to factor an integer N, Shor's algorithm runs in polynomial time (the time taken is polynomial in log N, which is the size of the input). Specifically it takes time O((log N)3), demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP. This is substantially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time — about O(e1.9 (log N)1/3 (log log N)2/3). The efficiency of Shor's algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squarings.If a quantum computer with a sufficient number of qubits could operate without succumbing to noise and other quantum decoherence phenomena, Shor's algorithm could be used to break public-key cryptography schemes such as the widely used RSA scheme. RSA is based on the assumption that factoring large numbers is computationally infeasible. So far as is known, this assumption is valid for classical (non-quantum) computers; no classical algorithm is known that can factor in polynomial time. However, Shor's algorithm shows that factoring is efficient on an ideal quantum computer, so it may be feasible to defeat RSA by constructing a large quantum computer. It was also a powerful motivator for the design and construction of quantum computers and for the study of new quantum computer algorithms. It has also facilitated research on new cryptosystems that are secure from quantum computers, collectively called post-quantum cryptography.In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored 15 into 3 × 5, using an NMR implementation of a quantum computer with 7 qubits.However, some doubts have been raised as to whether IBM's experiment was a true demonstration of quantum computation, since no entanglement was observed.Since IBM's implementation, several other groups have implemented Shor's algorithm using photonic qubits, emphasizing that entanglement was observed. In 2012, the factorization of 15 was repeated. Also in 2012, the factorization of 21 was achieved, setting the record for the largest number factored with a quantum computer. In April 2012, the factorization of 143 was achieved, although this used adiabatic quantum computation rather than Shor's algorithm. [1]".
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• Shor's_algorithm wikiPageExternalLink paper.tex.
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• Shor's_algorithm hasPhotoCollection Shor's_algorithm.
• Shor's_algorithm subject Category:Articles_containing_proofs.
• Shor's_algorithm subject Category:Integer_factorization_algorithms.
• Shor's_algorithm subject Category:Quantum_algorithms.
• Shor's_algorithm subject Category:Quantum_information_science.
• Shor's_algorithm type Abstraction100002137.
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• Shor's_algorithm type IntegerFactorizationAlgorithms.
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• Shor's_algorithm comment "Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm (an algorithm that runs on a quantum computer) for integer factorization formulated in 1994. Informally it solves the following problem: Given an integer N, find its prime factors.On a quantum computer, to factor an integer N, Shor's algorithm runs in polynomial time (the time taken is polynomial in log N, which is the size of the input).".
• Shor's_algorithm label "Algorithme de Shor".
• Shor's_algorithm label "Algoritme van Shor".
• Shor's_algorithm label "Algoritmo de Shor".
• Shor's_algorithm label "Algoritmo di fattorizzazione di Shor".
• Shor's_algorithm label "Algorytm faktoryzacji Shora".
• Shor's_algorithm label "Shor's algorithm".
• Shor's_algorithm label "Shor-Algorithmus".
• Shor's_algorithm label "Алгоритм Шора".
• Shor's_algorithm label "خوارزمية شوور".
• Shor's_algorithm label "秀爾演算法".
• Shor's_algorithm sameAs Shor-Algorithmus.
• Shor's_algorithm sameAs Algoritmo_de_Shor.
• Shor's_algorithm sameAs Algorithme_de_Shor.
• Shor's_algorithm sameAs Algoritmo_di_fattorizzazione_di_Shor.
• Shor's_algorithm sameAs 쇼어_알고리즘.
• Shor's_algorithm sameAs Algoritme_van_Shor.
• Shor's_algorithm sameAs Algorytm_faktoryzacji_Shora.
• Shor's_algorithm sameAs m.0bqgp.
• Shor's_algorithm sameAs Q940334.
• Shor's_algorithm sameAs Q940334.
• Shor's_algorithm sameAs Shor's_algorithm.
• Shor's_algorithm wasDerivedFrom Shor's_algorithm?oldid=604628263.
• Shor's_algorithm isPrimaryTopicOf Shor's_algorithm.